Rotating 28501

Which bags shaped like the shell of a rotating cone can hold the most popcorn? The first bag has a height of 20 cm, and the length of its side is 24 cm. The second bag has a base radius of 10 cm and a height of 25 cm.

Correct answer:

x =  1

Step-by-step explanation:

$$\begin{gathered} h_1=20\text{cm} \\ {s}_1=24\text{cm} \\ {r}_2=10\text{cm} \\ {h}_2=25\text{cm} \\ {r}_1=\sqrt{s_1^2-h_1^2}=\sqrt{24^2-20^2}=4\sqrt{11}\text{cm}\doteq 13.2665\text{cm} \\ {V}_1=\frac{1}{3}\cdot \pi \cdot r_1^2\cdot h_1=\frac{1}{3}\cdot 3.1416\cdot 13.2665^2\cdot 20\doteq 3686.1354 \\ {V}_2=\frac{1}{3}\cdot \pi \cdot r_2^2\cdot h_2=\frac{1}{3}\cdot 3.1416\cdot 10^2\cdot 25\doteq 2617.9939 \\ {V}_1>V_2 \\ x=1 \end{gathered}$$

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